Problem: Simplify the following expression: $ a = \dfrac{4z}{5z - 1} + \dfrac{-7}{5} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{4z}{5z - 1} \times \dfrac{5}{5} = \dfrac{20z}{25z - 5} $ Multiply the second expression by $\dfrac{5z - 1}{5z - 1}$ $ \dfrac{-7}{5} \times \dfrac{5z - 1}{5z - 1} = \dfrac{-35z + 7}{25z - 5} $ Therefore $ a = \dfrac{20z}{25z - 5} + \dfrac{-35z + 7}{25z - 5} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{20z - 35z + 7}{25z - 5} $ $a = \dfrac{-15z + 7}{25z - 5}$